Download Induced EMF = -N ΔΦ / Δt This is Faraday`s law. The minus sign is

Faraday’s Law Notes
According to most text books, the induction rule is referred to as Faraday’s Law of
induction. The directional sense (since EMF is not a vector we are careful not to say
direction) of the induced EMF is referred to as Lenz’ Law.
Ghost magnet – this is a semi-popular concept/term to help describe the sense of the
induced current. The induced EMF produces a current in the coil, which has an
associated magnet. This ghost magnet is always induced in such a manner as to
oppose the change in the inducing field. This information helps us determine the
direction of current flow (clockwise/ counter-clockwise as viewed from the end of the
coil) and gives the directional sense of Lenz’ law.
Terminology:
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The induced EMF depends upon the change in a quantity called magnetic flux.
B goes by several names – magnetic field, magnetic flux density, and a few other
less common names.
B is measured using the SI unit of Tesla, or Webber per square meter. The unit
of magnetic flux is the Webber.
The desired connection to be made here is that a quantity called magnetic flux is
defined in a technical way, but amounting to the net number of B lines passing
through the area of the coil is the important quantity. If B is perpendicular to the
area (like a pencil pointing up from a table top) then the flux is simply B multiplied
by the Area. If B and A are not perpendicular, then the angles must be taken into
account. At the high school level we will only deal with situations where B is
perpendicular to A.
We are normally dealing with one or more “flat” area—coils. If the area is closed,
like the area of a sphere, then the number of flux lines will be zero, since each B
line that passes in through the area will also eventually pass out of the closed
area. This is a result of the fact that B fields loop back upon themselves.
Induced EMF = -N ΔΦ / Δt This is Faraday’s law. The minus sign is often referred to as
Lenz’ law. N is the number of turns in the coil.
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Φ is magnetic flux, the net number of field lines passing through the coil area.
The shape of the coil is not important; its area is expressed in square meters (m2).
Magnetic flux is equal to the product of the magnetic field and coil area (Φ = B·A).
The EMF is induced, even if the coil is not there. However there will be no
current flow with out the presence of wires. Said again – the EMF is induced
whether the area with changing magnetic flux has a coil or not.
The EMF is not induced at a specific location like a battery, but rather like an
electric field around the loop. The EMF pushes the charged particles around the
loop.
Some situations may be described in terms studied in the past or in terms of Faraday’s
law. The point to be made is that Faraday’s law is more general and does not
contradict previous knowledge. An important example of this concept is the movement
of a wire through a magnetic field.
Consider the diagram at right with the B field out of the
page. The value of the induced voltage is
EMF = BLv
where B is the magnetic field strength, L is the length of
the wire on the right side of the coil “cutting” through the
B field, and v is the velocity of the loop. This equation
can be derived by two ways. The first recognizes that the change in area per time
containing magnetic field ΔA/Δt = Lv, leading to the equation above. A second way is to
realize that the force on the on charges in the wire F=qvB, leading to an induced electric
field E=vB, and since EL=EMF, the value of the EMF again becomes EMF=BLv.
There are several ways that the flux can change
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The size of the magnetic field can change – magnet approaches, electromagnet
changes
The size of the area can change – like coil above or some other possibilities
The orientation of the area relative to the field can change – coil rotating in field
The number of turns changing would be unusual but would change the EMF
Example Problem:
Find the EMF induced in a coil measuring 10 cm on each side that lies on a table, if the
average magnetic field into the table changes from 5 mT to 2 mT in 0.2 seconds.
L = .1 m
B1 = 5 x 10-3 T
B2 = 2 x 10-3 T
Δt = 0.2 s
EMF = A ΔB/Δt =